Question: All of the 3rd grade teachers and students from Loyola went on a field trip to an art museum. Tickets were $$5.50$ each for teachers and $$3.00$ each for students, and the group paid $$29.00$ in total. The next month, the same group visited a science museum where the tickets cost $$22.00$ each for teachers and $$11.50$ each for students, and the group paid $$113.00$ in total. Find the number of teachers and students on the field trips.
Explanation: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${5.5x+3y = 29}$ ${22x+11.5y = 113}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-22x-12y = -116}$ ${22x+11.5y = 113}$ Add the top and bottom equations together. $ -0.5y = -3 $ $ y = \dfrac{-3}{-0.5}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $ {5.5x+3y = 29}$ to find $x$ ${5.5x + 3}{(6)}{= 29}$ $5.5x+18 = 29$ $5.5x = 11$ $x = \dfrac{11}{5.5}$ ${x = 2}$ You can also plug ${y = 6}$ into $ {22x+11.5y = 113}$ and get the same answer for $x$ ${22x + 11.5}{(6)}{= 113}$ ${x = 2}$ There were $2$ teachers and $6$ students on the field trips.